Horner, best known for scoring the movie "Titanic," was "an avid and experienced pilot," the statement from the Gorfaine/Schwartz agency said.
The Hollywood Reporter reported his death, attributing the confirmation to Sylvia Patrycja, his assistant.
"A great tragedy has struck my family today, and I will not be around for a while. I would like some privacy and time to heal," Horner's assistant, Sylvia Patrycja posted on her Facebook page
"We have lost an amazing person with a huge heart, and unbelievable talent. He died doing what he loved. Thank you for all your support and love and see you down the road. Love Sylvia."
Condolences pour in
Horner won two Oscars for his work on the 1997 James Cameron-directed "Titanic" -- earning best original dramatic score and best original song for the Celine Dion classic, "My Heart Will Go On."
He was nominated for Academy Awards 10 times and wrote the music for numerous blockbusters, including "Braveheart," "Apollo 13" and "The Amazing Spider-Man." He collaborated again with Cameron for 2009's "Avatar," the top-grossing film of all time.
Reaction to his reported death was immediate, with celebrities who worked with him posting condolences.
"Brilliant Composer James Horner, friend & collaborator on 7 movies has tragically died in a plane crash. My heart aches for his loved ones," tweeted Ron Howard, who directed "Apollo 13."
Leona Lewis, who worked with Horner on the theme for "Avatar," said working with the composer "was one of the biggest moments of my life."
"He was such a kind soul, I'm so saddened," she tweeted.
The single-engine S312 Tucano crashed under unknown circumstances near Cuyama, about 60 miles north of Santa Barbara, on Monday morning, the Federal Aviation Administration said.
The debris field from the crash was scattered across a roughly 1-acre area in a dry riverbed, said Mike Eliason, a spokesman for the Santa Barbara County Fire Department.
The aircraft caught fire on impact, and the flames spread to the surrounding vegetation, he said.
More than 75 films
Horner was born in 1953 in Los Angeles, but he grew up in England, studying piano at London's Royal College of Music. He moved back to the United States to attend college, earning a music degree from the University of Southern California, and then his master's and doctorate from UCLA.
Horner composed music for more than 75 films, making his feature-film debut in 1982 in "Star Trek II: The Wrath of Khan."
In addition to the accolades he earned for "Titanic," Horner won Grammy Awards for "Somewhere Out There" from "An American Tail" in 1987 and "Glory" in 1990. He also composed the music for such 1980s classics as "Field of Dreams," "Cocoon" and James Cameron's "Aliens" in 1986.
Horner leaves behind a wife, Sarah, and two daughters.